Derivatives of trigonometric functions cheat sheet, Cheat Sheet of Calculus

Download Derivatives of trigonometric functions cheat sheet and more Cheat Sheet Calculus in PDF only on Docsity! Mathematics Learning Centre Derivatives of trigonometric functions Christopher Thomas University of Sydney Mathematics Learning Centre, University of Sydney 1 1 Derivatives of trigonometric functions To understand this section properly you will need to know about trigonometric functions. The Mathematics Learning Centre booklet Introduction to Trigonometric Functions may be of use to you. There are only two basic rules for differentiating trigonometric functions: d dx sin x = cos x d dx cos x = − sin x. For differentiating all trigonometric functions these are the only two things that we need to remember. Of course all the rules that we have already learnt still work with the trigonometric functions. Thus we can use the product, quotient and chain rules to differentiate functions that are combinations of the trigonometric functions. For example, tan x = sin x cos x and so we can use the quotient rule to calculate the derivative. f(x) = tan x = sin x cos x , f ′(x) = cos x.(cos x) − sin x.(− sin x) (cos x)2 = cos2 x + sin2 x cos x = 1 cos2 x (since cos2 x + sin2 x = 1) = sec2 x Note also that cos2 x + sin2 x cos2 x = cos2 x cos2 x + sin2 x cos2 x = 1 + tan2 x so it is also true that d dx tan x = sec2 x = 1 + tan2 x.